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Math Help - Simple matrix problem

  1. #1
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    Simple matrix problem

    Given the system:

    3x + y + z + v = b1
    x - y + z + v = b2
    x + y - z + v = b3
    x + y + z - v = b4

    Fint the values for b1,b2,b3,b4 for which the system is consistent, in the form:

    a1 * b1 + a2 * b2 + a3 * b3 + a4 * b4 = 0

    and the answer is the row vector [a1,a2,a3,a4].

    Solve the system with the values previously found, in the form:

    |x| | b1 |
    |y| | b2 |
    |z| = C | b3 | + t * d
    |v| | b4 |

    Thanks!
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  2. #2
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    Here's what I've got so far. The augmented matrix for the system is:

    3 1 1 1 b1
    1 -1 1 1 b2
    1 1 -1 1 b3
    1 1 1 -1 b4

    reduced eschelon form I made to be:

    1 1/3 1/3 1/3 (1/3b1)
    0 1 -1/2 -1/2 (-3/4b2 + 1/4b1)
    0 0 1 -1 -b3 (-1/2b2 + 1/2b1)
    0 0 0 0 (-5/6b1 + 3/4b2 + 4/3b3 + 1/2b4)

    Which means -5/6b1 + 3/4b2 + 4/3b3 + 1/2b4 has to equal 0 for the system to be consistent, and the final answer should be:

    [-5/6,3/4,4/3,1/2]

    Is there a quick way to check the answer? Also, how do I solve the system with the values previously found, in the form:

    |x|..... | b1 |
    |y|..... | b2 |
    |z| = C| b3 | + t * d
    |v|......| b4 |

    Thanks!
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  3. #3
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    Well, now I now that this reduced echelon form

    1 1/3 1/3 1/3 (1/3b1)
    0 1 -1/2 -1/2 (-3/4b2 + 1/4b1)
    0 0 1 -1 -b3 (-1/2b2 + 1/2b1)
    0 0 0 0 (-5/6b1 + 3/4b2 + 4/3b3 + 1/2b4)

    is wrong, but I don't know where I did something wrong... any help?
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